Computing Voronoi Adjacencies in High Dimensional Spaces by Using Linear Programming

Conference paper

DOI: 10.1007/978-1-4614-5076-4_3

Volume 30 of the book series Springer Proceedings in Mathematics & Statistics (PROMS)
Cite this paper as:
Mendez J., Lorenzo J. (2013) Computing Voronoi Adjacencies in High Dimensional Spaces by Using Linear Programming. In: Latorre Carmona P., Sánchez J., Fred A. (eds) Mathematical Methodologies in Pattern Recognition and Machine Learning. Springer Proceedings in Mathematics & Statistics, vol 30. Springer, New York, NY

Abstract

Some algorithms in Pattern Recognition and Machine Learning as neighborhood-based classification and dataset condensation can be improved with the use of Voronoi tessellation. This paper shows the weakness of some existing algorithms of tessellation to deal with high-dimensional datasets. The use of linear programming can improve the tessellation procedures by focusing on Voronoi adjacency. It will be shown that the adjacency test based on linear programming is a version of the polytope search. However, the polytope search procedure provides more information than a simple Boolean test. This paper proposes a strategy to use the additional information contained in the basis of the linear programming algorithm to obtain other tests. The theoretical results are applied to tessellate several random datasets, and also for much-used datasets in Machine Learning repositories.

Keywords

Voronoi adjacencies Nearest neighbors Machine learning Linear programming 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Departamento de Informática y SistemasUniversity Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain
  2. 2.Institute of Intelligent SystemsUniversity Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain